Process for Computing a Frequency Offset for a UMTS Communication System Based on the CPICH Pilot Signals

ABSTRACT

Process for computing an estimation of the frequency offset in a receiver for a UMTS communication network said receiver receives the signal transmitted by two antennas and including two Common Pilot CHannels (CPICH), said process involving the steps of separating the two signals by means of computation and computing the frequency offset on the base of the two separated signals

TECHNICAL FIELD

The invention relates to the field of wireless communication and moreparticularly to a process for estimating the frequency offset in thirdgeneration wireless communication systems, particularly for UMTS.

BACKGROUND ART

Universal Mobile Telecommunications Systems (UMTS) is based on theW-CDMA technology and is in the heart of the 3G communication networksproviding packet based transmission of text, digitized voice, andmultimedia data at rates up to 2 Megabits per second.

One particular case of UMTS is defined in the 3G specification, whereone base station of such a communication systems may comprise twoemitting antennas each transmitting one signal comprising onecorresponding Common Pilot CHannel (CPICH). The transmitted sequence ofpilots from each antenna is constructed by applying a sign pattern givenby FIG. 1 to the symbol(1+j), where j is to the imaginary complex suchas j²=−1.

FIG. 1: This figure represents the pattern of the transmitted CPICHpilots' sequence.

Those two pilot signals which are transmitted by the base station areused for the determination of the channel characteristics but also forestimating the frequency offset between the base station reference clockand the internal clock of the User Equipment (UE). The received signalcorresponding to the transmission of the k^(th) pilot sample in theabsence of frequency offset is given by:

${r\lbrack k\rbrack} = {{\left( {1 + j} \right)\left( {{h_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{h_{2}\lbrack k\rbrack}}} \right)} + {n\lbrack k\rbrack}}$

while when the UE is subject to a frequency offset with respect to thebase station, the received signal is then

${r\lbrack k\rbrack} = {{\left( {1 + j} \right)\left( {{h_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{h_{2}\lbrack k\rbrack}}} \right){\exp \left( {{j\; 2\pi \; k\; \Delta \; f\; T} + \phi_{0}} \right)}} + {n\lbrack k\rbrack}}$

Where h_(m)[k] corresponds to the channel response from antenna m (m=1,2) and at the time instant of transmission of the k^(th) pilot, Δf isthe frequency offset, T is the time duration between two consecutivesamples and φ₀ is an initial phase rotation.

Some techniques are already known for computing an estimation of thefrequency offset based on the computation of phase discriminator.

However, the techniques which are known do not achieve both accuracy inthe estimation of the offset and still operate in a relatively widerange of frequency offsets.

It is particularly desirable to be able to estimate an offset in themaximum range allowed by an estimation based on the CPICH, whileproviding accuracy in the estimation. This maximum range is given by

${{{\Delta \; f}} \leq \frac{1}{2T}},$

where T is the time between two consecutive CPICH pilots. In UMTS

$T = {\frac{1}{15}10^{- 3}}$

seconds, which corresponds to covering a range of frequency offsets fromminus to plus 7500 Hz.

Such is the goal of the present invention.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an efficientfrequency offset estimation method which is suitable for direct-sequence(DS) spread-spectrum systems and particularly for the 3GPP UMTSstandard.

It is a further object of the present invention to provide a methodwhich provides both accuracy and wide range of estimation of thefrequency offset.

It is another object of the present invention to provide a receiver fora UMST communication system which incorporates improved frequency offsetestimation mechanisms.

These and other objects of the invention are achieved by means of aprocess for computing an estimation of the frequency offset whichinvolves a pre-processing based on the separation at the receiver of thetwo pilot signals transmitted from the two antennas by means of thecomputation of

$\begin{matrix}{{r_{NoTxd}\lbrack k\rbrack} = {{r\lbrack k\rbrack} + {r\left\lbrack {k + 2} \right\rbrack}}} \\{= {{\left( {1 + j} \right)\left( {{S_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{2}\lbrack k\rbrack}}} \right)} + {N_{s}\lbrack k\rbrack}}}\end{matrix}$ $\begin{matrix}{{r_{Txd}\lbrack k\rbrack} = {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {{r\lbrack k\rbrack} - {r\left\lbrack {k + 2} \right\rbrack}} \right)}} \\{= {{\left( {1 + j} \right)\left( {{S_{2}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{1}\lbrack k\rbrack}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{N_{d}\lbrack k\rbrack}}}}\end{matrix}$

Where

r[k] is the received signal at the instant k;

Where r_(NoTxd) and r_(Txd) are the received pilot signals from antenna1 and from antenna 2 respectively, assuming that the channel does notchange (i.e. h₁[k]=h₁ and h₂[k]=h₂) and where for m=1,2:

S _(m) [k]=h _(m) exp(jφ ₀)(exp(jkΦ)+exp(j(k+2)Φ)),

D _(m)[2k]=h _(m) exp(jφ ₀)(exp(jkΦ)−exp(j(k+2)Φ))

N _(s) [k]=n[k]+n[k+2]

N _(d) [k]=n[k]−n[k+2]

and Φ=2 π Δf T

we then compute

R _(r) _(NoTxd) _(r) _(NoTxd) [k]=r _(NoTxd) [k]*conj(r _(NoTxd) [k+1])

R _(r) _(Txd) _(r) _(Txd) [k]=r _(Txd) [k]*conj(r _(Txd) [k+1])

where conj(.) is the complex conjugate operator.

With the assumption that the channel does not change (i.e. h₁[k]=h₁ andh₂[k]=h₂) and after simplification, we have

${R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack} = {{2\begin{pmatrix}{R_{S_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{2}D_{2}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}}\end{pmatrix}} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{2\begin{pmatrix}{R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{1}D_{1}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}}\end{pmatrix}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}$

where, for m=1,2 and n=1,2

R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))

R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))

R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)

R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])

R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1])

In one embodiment, the estimation is based on one estimatorR_(even, avr) computed in accordance with the following formulas:

$R_{{even},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{14mu} {even}}}^{N_{2}}\left( {{R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} + {R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack}} \right)}}$

which simplifies to:

$R_{{even},{avr}} = {{4\; {\exp \left( {j\; \Phi} \right)}\left( {{h_{1}}^{2} + {h_{2}}^{2}} \right){\cos \left( {2\Phi} \right)}} + {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{11mu} {even}}}^{N_{2}}\left( {{R_{N_{s}N_{s}}\lbrack k\rbrack} - {R_{N_{d}N_{d}}\lbrack k\rbrack}} \right)}}}$

where N₁ and N₂ are respectively the indices of the first and the lastCPICH symbols used for the frequency offset estimation. The use of theaverage tends to attenuate the effect of noise by averaging over severalsymbols.

The frequency offset estimate being provided by the formula:

${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m\left( R_{{even},{avr}} \right)}}{\Re \; {e\left( R_{{even},{avr}} \right)}} \right)}}$

where

(.) and ℑm(.) are respectively the imaginary part and real partoperators. Alternatively, the frequency offset estimation is based onone estimator R_(odd, avr) computed in accordance with the followingformulas:

$R_{{odd},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{14mu} {odd}}}^{N_{2}}\left( {{R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} + {R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack}} \right)}}$

which simplifies to

$R_{{odd},{avr}} = {{4\; {\exp \left( {j\; \Phi} \right)}\left( {{h_{1}}^{2} + {h_{2}}^{2}} \right)} + {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{11mu} {odd}}}^{N_{2}}\left( {{R_{N_{s}N_{s}}\lbrack k\rbrack} + {R_{N_{d}N_{d}}\lbrack k\rbrack}} \right)}}}$

where N₁ and N₂ are respectively the indices of the first and the lastpilot symbols used for the frequency offset estimation. The use of theaverage tends to attenuate the effect of noise by averaging over severalsymbols.

The frequency offset estimate being provided by the formula:

${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m\left( R_{{odd},{avr}} \right)}}{\Re \; {e\left( R_{{odd},{avr}} \right)}} \right)}}$

In one particular, embodiment, the estimation is computed on the basisof both R_(odd, avr) and R_(even, avr) in accordance with the formula:

If

(R _(odd, avr))|>|ℑm(R _(odd, avr))|

R=R _(odd, avr) +R _(even, avr)

else

R=R _(odd, avr) −R _(even, avr)

and the frequency offset estimate being provided by the formula:

${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m(R)}}{\Re \; {e(R)}} \right)}}$

The invention also provides a process for processing the CPICH pilotsignals r(i) received from the two antennas of a base station whichinvolves the steps:

extracting the received CPICH signal included in the CPICH channel;

performing a first processing branch (left) comprising the steps of:

-   -   computing a first intermediate value x(i) in accordance with the        formula:

x(i)=r(i)+r(i+2)

-   -   computing a second intermediate value y(i) derived from the        first intermediate value x(i) in accordance with the formula:

y(i)=x(i). x*(i+1)

-   -   where x*(i+1) is the complex conjugate of x(i+1)

performing a second processing branch (right) comprising the steps of:

-   -   computing a third intermediate value x′(i) in accordance with        the formula:

x′(i)=r(i)−r(i+2)

-   -   computing a fourth intermediate value t(i) derived from the        third intermediate value x′(i) in accordance with the formula:

t′(2k)=x′(2k) and

t′(2k+1)=−x′(2k+1)

-   -   computing a fifth intermediate value y′(i) derived from the        fourth intermediate value t′(i) in accordance with the formula:

y′(i)=t′(i). t′*(i+1)

computing a sixth and seventh intermediate values Z and Z′ in accordancewith the formulas:

Z(2k)=y(2k)+y′(2k)

Z′(2k+1)=y(2k+1)+y′(2k+1)

respectively computing an eight and a ninth values S and S′ inaccordance with the following formulation:

S=1/N Σ Z(k) for k=1 to N

S′=1/N Σ Z′(k) for k=1 to N

performing a test to determine whether the absolute value of the realpart of S′ is superior to the absolute value of the imaginary part of S′and, in that case, computing (30) a tenth intermediate value R asfollows:

R=S′+S

And, conversely if the absolute value of the real part of S′ is inferiorto the absolute value of the imaginary part of S′, computing R inaccordance with the formula:

R=S′−S

The offset estimation is then simply computed as follows:

${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m(R)}}{\Re \; {e(R)}} \right)}}$

where

(R) and ℑm(R) are the real and imaginary parts, respectively of thetenth intermediate value R.

The invention is particularly suitable for the achievement of a UMTSreceiver of a User Equipment (UE) such as a mobile telephone or aPortable Document Assistant.

DESCRIPTION OF THE DRAWINGS

Other features of one or more embodiments of the invention will best beunderstood by reference to the following detailed description when readin conjunction with the accompanying drawings.

FIG. 1 illustrates the structure of the sign patter (applied to (1+j))of the two CPICH pilots sequences which are used in the UMTS usingtransmit diversity (TxD)

FIG. 2 illustrates one embodiment of the method for computing the offsetfrequency in accordance with the present invention.

FIG. 3 illustrates the principle of the separation of the two signalstransmitted through the two emitting antennas.

FIG. 4 illustrates the Root Mean Square Error (RMSE) of the frequencyoffset estimation (FOE) as a function of the frequency offset (FO) foran AWGN environment and SNR=0 dB

FIG. 5 illustrates the RMSE of the frequency offset estimation as afunction of lor/loc, in an AWGN environment and for FO=0 Hz

FIG. 6 illustrates the RMSE of the frequency offset as a function oflor/loc, in case 1 environment (defined in the 3GPP specs) and for FO=0Hz.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The invention can be implemented in digital electronic circuitry forminga mobile telephone or a Portable Digital Assistant (PDA) includinghardware circuits with a combination of firmware and software.

The method which is proposed is based on the computation of the phasediscriminator, that is to say the sum of the autocorrelation of thesamples sequence.

To simplify the mathematical treatment, we use a symbol-rate model forthe CPICH symbols transmitted from Tx antenna 1 and Tx antenna 2 insymbol time instants k=0,1, . . . , 149 . . . , during one 10-ms radioframe, which reads:

p₁[k] = (1 + j)${p_{2}\lbrack k\rbrack} = {\left( {1 + j} \right)\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}}$

FIG. 1 illustrates the sign pattern (applied to (1+j)) resulting fromthose formulas.

These Tx symbols are transmitted via time-varying channel coefficientsto obtain the effective received symbol (on one single Rx antenna) intime instants, described by k=0,1, . . . , 149.

r[k] = (h₁[k]p₁[k] + h₂[k]p₂[k])exp ((j 2π k Δ f T + ϕ₀)) + n[k]${r\lbrack k\rbrack} = {{\left( {1 + j} \right)\left( {{h_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{h_{2}\lbrack k\rbrack}}} \right){\exp \left( \left( {{j\; 2\pi \; k\; \Delta \; f\; T} + \phi_{0}} \right) \right)}} + {n\lbrack k\rbrack}}$

where h_(m)[k] is the channel gain from antenna m at time instant k andn[k] is the additive Gaussian noise with zero mean and variance σ².

Δf corresponds to the frequency offset and assumed to be identical forboth antennas.

The method is based on a separation of the received pilot signals fromthe two transmit antennas—summarized in FIG. 3—in order to keep thesampling period of the resulting samples equal to T, which is acondition for keeping a relatively wide estimation of frequency offsets.

Now considering r_(NoTxd) and r_(Txd)[k] being the computed signalsrespectively containing only the pilot transmitted from antenna 1 andantenna 2, computed write the following formula:

$\mspace{65mu} {{r_{NoTxd}\lbrack k\rbrack} = {{{r\lbrack k\rbrack} + {r\left\lbrack {k + 2} \right\rbrack}} = {{\left( {1 + j} \right)\left( {{S_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{2}\lbrack k\rbrack}}} \right)} + {N_{2}\lbrack k\rbrack}}}}$${r_{Txd}\lbrack k\rbrack} = {{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {{r\lbrack k\rbrack} - {r\left\lbrack {k + 2} \right\rbrack}} \right)} = {{\left( {1 + j} \right)\left( {{S_{2}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{1}\lbrack k\rbrack}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{N_{d}\lbrack k\rbrack}}}}$

Where for m=1,2

S _(m) [k]=h _(m) exp(jφ ₀)(exp(jkΦ)+exp(j(k+2)Φ))

D _(m)[2k]=h _(m) exp(jφ ₀)(exp(jkΦ)−exp(j(k+2)Φ))

N _(s) [k]=n[k]+n[k+2]

N _(d) [k]=n[k]−n[k+2]

h_(m) corresponding to the channel response for antenna m (m=1, 2),

j corresponding to the imaginary complex such as j²=−1 and Φ=2 π Δf T

It can be seen that the sampling period of r_(NoTxd) and r_(Txd)[k]sequences is T, which will allow a possible estimation range of

${{\Delta \; f}} \leq \frac{1}{2T}$

We then compute R_(NoTxd)[k] and R_(Txd)[k] from the separated signalr_(NoTxd) and r_(Txd)[k] as

R _(r) _(NoTxd) _(r) _(NoTxd) [k]=r _(NoTxd) [k]*conj(r _(NoTxd) [k+1])

R _(r) _(Txd) _(r) _(Txd) [k]=r _(Txd) [k]*conj(r _(Txd) [k+1])

which simplifies, with the assumption that the channel is constant (i.e.h₁[k]=h₁ and h₂[k]=h₂), to

${R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack} = {{2\begin{pmatrix}{R_{S_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{2}D_{2}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}}\end{pmatrix}} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{2\begin{pmatrix}{R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{1}D_{1}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}}\end{pmatrix}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}$

where, for m=1,2 and n=1,2

R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))

R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))

R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)

R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])

R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1])

If k is even, one may demonstrate that:

R _(even) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r)_(NoTxd) [k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)cos(2Φ)+R _(N) _(s) _(N) _(s)[k]−R _(N) _(d) _(N) _(d) [k]

And if k is odd,

R _(odd) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r) _(NoTxd)[k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)+(R _(N) _(s) _(N) _(s) [k]+R _(N) _(d)_(N) _(d) [k])

In order to attenuate the noise effect, we compute an average overseveral samples of R_(even)[k] and R_(odd)[k] as

$\begin{matrix}\begin{matrix}{R_{{even},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{14mu} {even}}}^{N_{2}}{R_{even}\lbrack k\rbrack}}}} \\{= {{4\; {\exp ({j\Phi})}\left( {{h_{1}}^{2} + {h_{2}}^{2}} \right){\cos \left( {2\Phi} \right)}} +}} \\{{\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{14mu} {even}}}^{N_{2}}\left( {{R_{N_{s},N_{s}}\lbrack k\rbrack} - {R_{N_{d}N_{d}}\lbrack k\rbrack}} \right)}}}\end{matrix} \\\begin{matrix}{R_{{odd},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\mspace{14mu} {odd}}}^{N_{2}}{R_{odd}\lbrack k\rbrack}}}} \\{= {{4\; {\exp ({j\Phi})}\left( {{h_{1}}^{2} + {h_{2}}^{2}} \right)} + {\frac{1}{N_{2} + N_{1}}\sum\limits_{{k = N_{1}},{k\mspace{14mu} {odd}}}^{N_{2}}}}} \\{\left( {{R_{N_{s}N_{s}}\lbrack k\rbrack} + {R_{N_{d}N_{d}}\lbrack k\rbrack}} \right)}\end{matrix}\end{matrix}$

Both of these two sums R_(even, avr) and R_(odd, avr) can be consideredas independent estimators and the frequency offset estimation is givenrespectively by

${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m\left( R_{{even},\; {avr}} \right)}}{\; {e\left( R_{{even},\; {avr}} \right)}} \right)}}$and${\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m\left( R_{{odd},\; {avr}} \right)}}{\; {e\left( R_{{odd},\; {avr}} \right)}} \right)}}$

The one based on R_(even, avr) is dependent on the FO due to the cos(2Φ)and is expected to show poor results around

${\Phi } = {{\frac{\pi}{4}\mspace{14mu} {or}\mspace{14mu} {\Phi }} = \frac{3\; \pi}{4}}$(i.e.  FO = ±1875  or  FO = ±5625)

Also, it should be noticed that this cos(2Φ) introduces a sign inversionfor

${\Phi } \in \left\lbrack {\frac{\pi}{4},\frac{3\; \pi}{4}} \right\rbrack$

Thus, in one particular advantageous embodiment, the two discrimatorsvalues R_(even, avr) and R_(odd, avr) are accumulated as follows:

If

(R _(odd, avr))|>|ℑm(R _(odd, avr))|

R=R _(odd, avr) +R _(even, avr)

else

R=R _(odd, avr) −R _(even, avr)

The correlation R is passed to the arc tan function in order to extractthe is frequency offset estimate:

${{\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m(R)}}{\; {e(R)}} \right)}}}\mspace{11mu}$

With respect to FIG. 2, there is now described one particular embodimentof a method for computing the frequency offset Δf which provides bothaccuracy and a relatively wide range of frequency use.

In a step 21, the process extracts the received CPICH signal included inthe CPICH channel. As known in the art, it is assumed that the signalreceived at the antenna of the user equipment is properly equalized,de-spreaded and descrambled in accordance with the W-CDMA standard. Suchoperations are well known to a skilled man and, therefore, do not needfurther development. It suffices to recall that the received despreadedsignal is modulated with the appropriate code in order to extract thepredetermined CPICH channel. Such channel generates the sum of the twopilot signals transmitted by the base station.

From step 21, two parallel sequences are performed in order to separatethe two pilot channels, with a left branch based on steps 22-23 and aright branch based on steps 24-25-26.

Considering the left branch, one sees that the process proceeds to astep 22, the process proceeds with the computation of a firstintermediate value x(i) in accordance with the formula:

x(i)=r(i)+r(i+2)

It can be seen that step 21 achieves the computation of r_(NoTxd)[k]which was mentioned above:

${r_{NoTxd}\lbrack k\rbrack} = {{{r\lbrack k\rbrack} + {r\left\lbrack {k + 2} \right\rbrack}} = {{\left( {1 + j} \right)\left( {{S_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{2}\lbrack k\rbrack}}} \right)} + {N_{s}\lbrack k\rbrack}}}$

Then, in a step 23, the process proceeds with the computation of asecond intermediate value y(i) derived from the first intermediate valuex(i) in accordance with the formula:

y(i)=x(i). x*(i+1)

with x*(i+1) being the conjugate value of x(i+1).

Such second intermediate value corresponds to the computation of R_(r)_(NoTxd) _(r) _(NoTxd) [k] mentioned above.

Considering the right branch, one sees that, after completion of step21, the process proceeds to a step 24, the process proceeds with thecomputation of a third intermediate value x′(i) in accordance with theformula:

x′(i)=r(i)−r(i+2)

Then, in a step 25, the process proceeds with the computation of afourth intermediate value t(i) derived from the third intermediate valuex′(i) in accordance with the formula:

t′(2k)=x′(2k) and

t′(2k+1)=−x′(2k+1)

It can be seen that steps 24-25 achieves the computation of the value ofr_(txd)[k] which was mentioned above:

${r_{Txd}\lbrack k\rbrack} = {{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {{r\lbrack k\rbrack} - {r\left\lbrack {k + 2} \right\rbrack}} \right)} = {{\left( {1 + j} \right)\left( {{S_{2}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{1}\lbrack k\rbrack}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{N_{d}\lbrack k\rbrack}}}}$

Then, in a step 26, the process proceeds with the computation of a fifthintermediate value y′(i) derived from the fourth intermediate valuet′(i) in accordance with the formula:

y′(i)=t′(i). t′*(i+1)

where t′*(i+1) corresponds to the conjugate of the complex t′(i+1).

Step 26 achieves the computation of R_(r) _(Txd) _(r) _(Txd) [k]mentioned above

Then, in a step 27, the process proceeds with the computation of a sixthand seventh intermediate values, respectively Z and Z′ which arecomputed as follows:

Z(2k)=y(2k)+y′(2k)

Z′(2k+1)=y(2k+1)+y′(2k+1)

Then, in a step 28, the process proceeds with the average of the Z andZ′ value over a period of N samples in order to respectively generate aneight and a ninth values S and S′ in accordance with the followingformulation:

S=1/N Σ Z(k) for k=1 to N

S′=1/N Σ Z′(k) for k=1 to N

The process then proceeds with a step 29 which is a test for determiningwhether the absolute value of the real part of S′ is superior to theabsolute value of the imaginary part of S′, in which case, the processproceeds with a step 30 where the two values S and S′ are added in orderto generate a tenth intermediate value R as follows:

R=S′+S

The process then proceeds to a step 32.

If the absolute value of the real part of S′ is inferior to the absolutevalue of the imaginary part of S′ in step 29, the process proceeds to astep 31 where the value of S is subtracted from that of S′ in order tocompute R in accordance with the formula:

R=S′−S

After completion of steps 30 and 31, the process proceeds to a step 32where the frequency offset estimation is computed as follows:

${{\Delta \; f} = {\frac{1}{2\pi \; T}{\arctan \left( \frac{\; {m(R)}}{\; {e(R)}} \right)}}}\mspace{11mu}$

where

(R) and ℑm(R) are the real and imaginary parts, respectively of thetenth intermediate value R.

The method which was described above shows a sampling period of T, whichallows coverage of possible estimation range for a value of

${{\Delta \; f}} \leq \frac{1}{2T}$

FIGS. 4, 5 and 6 are comparative flow charts allowing comparison of theprocess of the invention which was described above (and referred to asscheme n°3) with respect of two prior art method, namely scheme 1 and 2.

FIG. 4 represents the Root Mean Squared Error (RMSE) of the frequencyoffset estimate (FOE) as a function of the frequency offset (FO) forAWGN and a SNR=0 dB. It should be noticed that a prior artmethod—referred to as scheme 2—only have limited performances to FO<3500Hz since this estimator cannot estimate larger FOs. The curve which isrepresented highlights the expected behaviors of the differentestimators. As expected, estimator 3 (which is the one of the invention)shows degraded performances around 1875 Hz and 5625 Hz which isequivalent to the degradation shown by scheme 2 around 3.5 KHz. However,our proposed estimator has performance very close to those of estimator2 for small FOs, which corresponds to the working regime after the AFCloop convergence. Estimator 2 has the advantage of covering a muchlarger interval.

FIGS. 5 and 6 plot the FOE's RMSE as a function of lor/loc for FO=0 Hz(for AWGN and case 1 propagation scenarios respectively).

The considered SPW simulations setups are as follows:

For AWGN:

Measurement Reference Channel: 12.2 Kbps

lorx/loc=−i dB

DPCH_Ec/lorx=−16.6 dB

loc=−60 dBm

For Fading Multi-Path Case 1:

Measurement Reference Channel: 12.2 Kbps lorx/loc=9 dB DPCH_Ec/lorx=−15dB loc=−60 dBm

Multi-path propagation: 2 paths

-   -   Powers: 0 dB, −10 dB    -   Delays: 0 ns, 976 ns

1. A process for computing an estimation of the frequency offset in areceiver for a UMTS communication network said receiver receives thesignal transmitted by two antennas and including two Common PilotCHannels (CPICH), said process involving a pre-processing based on theseparation of the two signals by means of the computation of${r_{NoTxd}\lbrack k\rbrack} = {{{r\lbrack k\rbrack} + {r\left\lbrack {k + 2} \right\rbrack}} = {{\left( {1 + j} \right)\left( {{S_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{2}\lbrack k\rbrack}}} \right)} + {N_{2}\lbrack k\rbrack}}}$${r_{Txd}\lbrack k\rbrack} = {{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {{r\lbrack k\rbrack} - {r\left\lbrack {k + 2} \right\rbrack}} \right)} = {{\left( {1 + j} \right)\left( {{S_{2}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{1}\lbrack k\rbrack}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{N_{d}\lbrack k\rbrack}}}}$Where r[k] is the received signal at the instant k; r_(NoTxd) andr_(Txd) are the result of said pre-processing; where for m=1,2S _(m) [k]=h _(m) exp(jφ ₀)(exp(jkΦ)+exp(j(k+2)Φ))D _(m)[2k]=h _(m) exp(jφ ₀)(exp(jkΦ)−exp(j(k+2)Φ))N _(s) [k]=n[k]+n[k+2]N _(d) [k]=n[k]−n[k+2] n[k] corresponding to the noise components in thereceived signal at instant k h_(m) corresponding to the channel responsefor antenna m (m=1, 2), j corresponding to the imaginary complex such asj²=−1 and Φ=2 π Δf T said pre-processing being then followed by anestimation of the frequency offset of the received signal.
 2. Theprocess according to claim 1 wherein the frequency offset estimation isbased on one estimator R_(even, avr) computed in accordance with thefollowing formulas:$R_{{even},\; {avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{even}}^{N_{2}}{R_{even}\lbrack k\rbrack}}}$withR _(even) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r)_(NoTxd) [k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)cos(2Φ)+R _(N) _(s) _(N) _(s)[k]−R _(N) _(d) _(N) _(d) [k] in which${R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack} = {{{r_{NoTxd}\lbrack k\rbrack}*{{conj}\left( {r_{NoTxd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\begin{pmatrix}{R_{s_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}D_{2}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}}\end{pmatrix}} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{{r_{Txd}\lbrack k\rbrack}*{{conj}\left( {r_{Txd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\begin{pmatrix}{R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}D_{1}}} +} \\{{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}}\end{pmatrix}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}}$where, for m=1,2 and n=1,2R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1]) The frequencyoffset estimate being provided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$3. The process according to claim 1 wherein the frequency offsetestimation is based on one estimator R_(odd, avr) computed in accordancewith the following formulas:$R_{{odd},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\; {odd}}}^{N_{2}}{R_{odd}\lbrack k\rbrack}}}$withR _(odd) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r) _(NoTxd)[k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)+(R _(N) _(s) _(N) _(s) [k]+R _(N) _(d)_(N) _(d) [k]) in which${R_{r_{{NoTxd}^{r}{NoTxd}}}\lbrack k\rbrack} = {{{r_{NoTxd}\lbrack k\rbrack}*{{conj}\left( {r_{NoTxd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{2}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}} \right)} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{{r_{Txd}\lbrack k\rbrack}*{{conj}\left( {r_{Txd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{1}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}}$where, for m=1,2 and n=1,2R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1]) The frequencyoffset estimate being provided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$4. The process according to claim 2 wherein the frequency offsetestimation is computed on the basis of both R_(odd, avr) andR_(even, avr) in accordance with the formula:If

(R _(odd, avr))|>|ℑm(R _(odd, avr))|R=R _(odd, avr) +R _(even, avr)elseR=R _(odd, avr) −R _(even, avr) and the frequency offset estimate beingprovided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$5. A process for computing an estimation of the frequency offset in areceiver for a UMTS communication network said receiver receives thesignal transmitted by two antennas and including two Common PilotCHannels (CPICH), said process involving the steps of: extracting thereceived CPICH signal included in the CPICH channel; performing a firstprocessing branch (left) comprising the steps of: computing a firstintermediate value x(i) in accordance with the formula:x(i)=r(i)+r(i+2) computing a second intermediate value y(i) derived fromthe first intermediate value x(i) in accordance with the formula:y(i)=x(i). x*(i+1) performing a second processing branch (right)comprising the steps of: computing a third intermediate value x′(i) inaccordance with the formula:x′(i)=r(i)−r(i+2) computing a fourth intermediate value t(i) derivedfrom the third intermediate value x′(i) in accordance with the formula:t′(2k)=x′(2k) andt′(2k+1)=−x′(2k+1) computing a fifth intermediate value y′(i) derivedfrom the fourth intermediate value t′(i) in accordance with the formula:y′(i)=t′(i). t′*(i+1) computing a sixth and seventh intermediate valuesZ and Z′ in accordance with the formulas:Z(2k)=y(2k)+y′(2k)Z′(2k+1)=y(2k+1)+y′(2k+1) respectively computing an eight and a ninthvalues S and S′ in accordance with the following formulation:S=1/N Σ Z(k) for k=1 to NS′=1/N Σ Z′(k) for k=1 to N performing a test to determine whether theabsolute value of the real part of S′ is superior to the absolute valueof the imaginary part of S′ and, in that case, computing a tenthintermediate value R as follows:R=S′+S And, conversely if the absolute value of the real part of S′ isinferior to the absolute value of imaginary part of S′, computing R inaccordance with the formula:R=S′−S Then, computing the offset estimation in accordance with theformula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$where

e(R) and ℑm(R) are the real and imaginary parts, respectively of thetenth intermediate value R.
 6. A receiver for a UMST communicationsystem comprising means for receiving the signals transmitted by twoantennas and including two Common Pilot CHannels (CPICH), said receivingcomprising means for separating the two signals based on the computationof:$\mspace{56mu} {{r_{NoTxd}\lbrack k\rbrack} = {{{r\lbrack k\rbrack} + {r\left\lbrack {k + 2} \right\rbrack}} = {{\left( {1 + j} \right)\left( {{S_{1}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{2}\lbrack k\rbrack}}} \right)} + {N_{s}\lbrack k\rbrack}}}}$${r_{Txd}\lbrack k\rbrack} = {{\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {{r\lbrack k\rbrack} - {r\left\lbrack {k + 2} \right\rbrack}} \right)} = {{\left( {1 + j} \right)\left( {{S_{2}\lbrack k\rbrack} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{D_{1}\lbrack k\rbrack}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}{N_{d}\lbrack k\rbrack}}}}$Where r[k] is the received signal at the instant k; r_(NoTxd) andr_(Txd) are the result of said pre-processing; Where for m=1,2S _(m) [k]=h _(m) exp(jφ ₀)(exp(jkΦ)+exp(j(k+2)Φ))D _(m)[2k]=h _(m) exp(jφ ₀)(exp(jkΦ)−exp(j(k+2)Φ))N _(s) [k]=n[k]+n[k+2]N _(d) [k]=n[k]−n[k+2] n[k] corresponding to the noise components in thereceived signal at instant k h_(m) corresponding to the channel responsefor antenna m (m=1, 2), j corresponding to the imaginary complex such asj²=−1 and Φ=2 π Δf T
 7. The receiver according to claim 6 wherein thefrequency offset estimation is based on one estimator R_(even, avr)computed in accordance with the following formulas:$R_{{even},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\; {even}}}^{N_{2}}{R_{even}\lbrack k\rbrack}}}$withR _(even) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r)_(NoTxd) [k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)cos(2Φ)+R _(N) _(s) _(N) _(s)[k]−R _(N) _(d) _(N) _(d) [k] in which${R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack} = {{{r_{NoTxd}\lbrack k\rbrack}*{{conj}\left( {r_{NoTxd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{2}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}} \right)} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{{r_{Txd}\lbrack k\rbrack}*{{conj}\left( {r_{Txd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{1}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}}$where, for m=1,2 and n=1,2R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1]) The frequencyoffset estimate being provided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$8. The process according to claim 6 wherein the frequency offsetestimation is based on one estimator R_(odd, avr) computed in accordancewith the following formulas:$R_{{odd},{avr}} = {\frac{1}{N_{2} - N_{1}}{\sum\limits_{{k = N_{1}},{k\; {odd}}}^{N_{2}}{R_{odd}\lbrack k\rbrack}}}$withR _(odd) [k]=R _(r) _(Txd) _(r) _(Txd) [k]+R _(r) _(NoTxd) _(r) _(NoTxd)[k]=4 exp(jΦ)(|h ₁|² +|h ₂|²)+(R _(N) _(s) _(N) _(s) [k]+R _(N) _(d)_(N) _(d) [k]) in which${R_{r_{NoTxd}r_{NoTxd}}\lbrack k\rbrack} = {{{r_{NoTxd}\lbrack k\rbrack}*{{conj}\left( {r_{NoTxd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{1}S_{1}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{2}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{S_{1}D_{2}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{2}S_{1}}}} \right)} + {R_{N_{s}N_{s}}\lbrack k\rbrack}}}$${R_{r_{Txd}r_{Txd}}\lbrack k\rbrack} = {{{r_{Txd}\lbrack k\rbrack}*{{conj}\left( {r_{Txd}\left\lbrack {k + 1} \right\rbrack} \right)}} = {{2\left( {R_{S_{2}S_{2}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{D_{1}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}R_{S_{2}D_{1}}} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}R_{D_{1}S_{2}}}} \right)} + {\left( {- 1} \right)^{\lfloor\frac{k + 1}{2}\rfloor}\left( {- 1} \right)^{\lfloor\frac{k + 2}{2}\rfloor}{R_{N_{d}N_{d}}\lbrack k\rbrack}}}}$where, for m=1,2 and n=1,2R _(S) _(m) _(S) _(m) =S _(m) [k].conj(S _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1+cos(2Φ)))R _(D) _(m) _(D) _(m) =D _(m) [k].conj(D _(m) [k+1])=2|h_(m)|²(exp(jΦ)(1−cos(2Φ)))R _(S) _(m) _(D) _(n) =S _(m) [k].conj(D _(n) [k+1])=−2jh _(m) h_(n)*exp(jΦ)sin(2Φ)R _(N) _(s) _(N) _(s) =N _(s) [k].conj(N _(s) [k+1])R _(N) _(d) _(N) _(d) =N _(d) [k].conj(N _(d) [k+1]) The frequencyoffset estimate being provided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$9. The receiver according to claim 7 wherein the frequency offsetestimation is computed based on both R_(odd, avr) and R_(even, avr) inaccordance with the formula:If

(R _(odd, avr))|>|ℑm(R _(odd, avr))|R=R _(odd, avr) +R _(even, avr)elseR=R _(odd, avr) −R _(even, avr) and the frequency offset estimate beingprovided by the formula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$10. A receiver for a UMTS communication network comprising means forreceiving the signal transmitted by two antennas and including twoCommon Pilot CHannels (CPICH), said receiver comprising: means forextracting the received CPICH signal included in the CPICH channel;means for performing a first processing branch (left) comprising thesteps of: means for computing a first intermediate value x(i) inaccordance with the formula:x(i)=r(i)+r(i+2) means for computing a second intermediate value y(i)derived from the first intermediate value x(i) in accordance with theformula:y(i)=x(i). x*(i+1) means for performing a second processing branch(right) comprising the steps of: means for computing a thirdintermediate value x′(i) in accordance with the formula:x′(i)=r(i)−r(i+2) means for computing a fourth intermediate value t(i)derived from the third intermediate value x′(i) in accordance with theformula:t′(2k)=x′(2k) andt′(2k+1)=−x′(2k+1) means for computing a fifth intermediate value y′(i)derived from the fourth intermediate value t′(i) in accordance with theformula:y′(i)=t′(i). t′*(i+1) means for computing a sixth and seventhintermediate values Z and Z′ in accordance with the formulas:Z(2k)=y(2k)+y′(2k)Z′(2k+1)=y(2k+1)+y′(2k+1) respectively computing an eight and a ninthvalues S and S′ in accordance with the following formulation:S=Σ Z(k) for k=1 to NS′=Σ Z′(k) for k=1 to N means for performing a test to determine whetherthe absolute value of the real part of S′ is superior to the absolutevalue of the imaginary part of S′ and, in that case, computing a tenthintermediate value R as follows:R=S′+S And, conversely if the absolute value of the real part of S′ isinferior to the absolute value of the imaginary part of S′, means forcomputing R in accordance with the formula:R=S′−S Means for computing the offset estimation in accordance with theformula:${\Delta \; f} = {\frac{1}{2\; \pi \; T}{\arctan \left( \frac{{m}(R)}{{e}(R)} \right)}}$where

e(R) and ℑm(R) are the real and imaginary parts, respectively of thetenth intermediate value R.
 11. The mobile telephone for a UMTScommunication network comprising the receiver as defined in claim
 6. 12.The mobile telephone according to claim 11 wherein it is embodied in aPortable Document Assistant (PDA).